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Definition df-nm 18105
Description: Define the norm on a group or ring (when it makes sense) in terms of the distance to zero. (Contributed by Mario Carneiro, 2-Oct-2015.)
Assertion
Ref Expression
df-nm  |-  norm  =  ( w  e.  _V  |->  ( x  e.  ( Base `  w )  |->  ( x ( dist `  w
) ( 0g `  w ) ) ) )
Distinct variable group:    x, w

Detailed syntax breakdown of Definition df-nm
StepHypRef Expression
1 cnm 18099 . 2  class  norm
2 vw . . 3  set  w
3 cvv 2788 . . 3  class  _V
4 vx . . . 4  set  x
52cv 1622 . . . . 5  class  w
6 cbs 13148 . . . . 5  class  Base
75, 6cfv 5255 . . . 4  class  ( Base `  w )
84cv 1622 . . . . 5  class  x
9 c0g 13400 . . . . . 6  class  0g
105, 9cfv 5255 . . . . 5  class  ( 0g
`  w )
11 cds 13217 . . . . . 6  class  dist
125, 11cfv 5255 . . . . 5  class  ( dist `  w )
138, 10, 12co 5858 . . . 4  class  ( x ( dist `  w
) ( 0g `  w ) )
144, 7, 13cmpt 4077 . . 3  class  ( x  e.  ( Base `  w
)  |->  ( x (
dist `  w )
( 0g `  w
) ) )
152, 3, 14cmpt 4077 . 2  class  ( w  e.  _V  |->  ( x  e.  ( Base `  w
)  |->  ( x (
dist `  w )
( 0g `  w
) ) ) )
161, 15wceq 1623 1  wff  norm  =  ( w  e.  _V  |->  ( x  e.  ( Base `  w )  |->  ( x ( dist `  w
) ( 0g `  w ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  nmfval  18111
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